Vanishing viscosity with short wave-long wave interactions for systems of conservation laws
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Publication:982306
DOI10.1007/s00205-009-0273-2zbMath1203.35020OpenAlexW2158397024MaRDI QIDQ982306
Hermano Frid, M. S. Figueira, João-Paulo Dias
Publication date: 6 July 2010
Published in: Archive for Rational Mechanics and Analysis (Search for Journal in Brave)
Full work available at URL: https://doi.org/10.1007/s00205-009-0273-2
Asymptotic behavior of solutions to PDEs (35B40) Singular perturbations in context of PDEs (35B25) Hyperbolic conservation laws (35L65) A priori estimates in context of PDEs (35B45) NLS equations (nonlinear Schrödinger equations) (35Q55)
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Cites Work
- Existence of local strong solutions for a quasilinear Benney system
- The Riemann problem for a class of hyperbolic conservation laws exhibiting a parabolic degeneracy
- Interaction equations for short and long dispersive waves
- The Cauchy problem for the system \(\partial_ tz - \partial_ x(\bar z^ y) = 0\)
- Plane waves in nonlinear electromagnetism
- Hyperbolic conservation laws with umbilic degeneracy. I
- Radially symmetric weak solutions for a quasilinear wave equation in two space dimensions
- EXISTENCE OF WEAK SOLUTIONS FOR A QUASILINEAR VERSION OF BENNEY EQUATIONS
- A General Theory for Interactions Between Short and Long Waves
- Nonstrictly hyperbolic systems of conservation laws of the conjugate type
- Well-posedness of the cauchy problem for the long wave-short wave resonance equations
- Weak solvability and well-posedness of a coupled Schrödinger-Korteweg de Vries equation for capillary-gravity wave interactions
- Front tracking for hyperbolic conservation laws
- Hyperbolic conservation laws with umbilic degeneracy
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